cp's OEIS Frontend

A331386 Numbers with at least one prime prime index.

%I A331386 #12 Feb 02 2021 04:35:35
%S A331386 3,5,6,9,10,11,12,15,17,18,20,21,22,24,25,27,30,31,33,34,35,36,39,40,
%T A331386 41,42,44,45,48,50,51,54,55,57,59,60,62,63,65,66,67,68,69,70,72,75,77,
%U A331386 78,80,81,82,83,84,85,87,88,90,93,95,96,99,100,102,105,108
%N A331386 Numbers with at least one prime prime index.
%C A331386 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A331386 The asymptotic density of this sequence is 1 - Product_{p in A006450} (1 - 1/p) = 1 - 1/(Sum_{n>=1} 1/A076610(n)) > 2/3. - _Amiram Eldar_, Feb 02 2021
%H A331386 Amiram Eldar, <a href="/A331386/b331386.txt">Table of n, a(n) for n = 1..10000</a>
%F A331386 A257994(a(n)) > 0.
%e A331386 The sequence of terms together with their prime indices begins:
%e A331386     3: {2}
%e A331386     5: {3}
%e A331386     6: {1,2}
%e A331386     9: {2,2}
%e A331386    10: {1,3}
%e A331386    11: {5}
%e A331386    12: {1,1,2}
%e A331386    15: {2,3}
%e A331386    17: {7}
%e A331386    18: {1,2,2}
%e A331386    20: {1,1,3}
%e A331386    21: {2,4}
%e A331386    22: {1,5}
%e A331386    24: {1,1,1,2}
%e A331386    25: {3,3}
%e A331386    27: {2,2,2}
%e A331386    30: {1,2,3}
%e A331386    31: {11}
%e A331386    33: {2,5}
%e A331386    34: {1,7}
%t A331386 Select[Range[100],MemberQ[FactorInteger[#],{_?(PrimeQ@*PrimePi),_}]&]
%Y A331386 Complement of A320628.
%Y A331386 Positions of terms > 0 in A257994.
%Y A331386 Positions of terms > 1 in A295665.
%Y A331386 Primes of prime index are A006450.
%Y A331386 Primes of nonprime index are A007821.
%Y A331386 Products of primes of prime index are A076610.
%Y A331386 Products of primes of nonprime index are A320628.
%Y A331386 The number of nonprime prime indices is given by A330944.
%Y A331386 Cf. A000040, A000720, A001222, A018252, A056239, A076610, A112798, A302242, A320633, A330943, A330944, A330947, A330949.
%K A331386 nonn
%O A331386 1,1
%A A331386 _Gus Wiseman_, Jan 17 2020